Blacksmith is definitely not the easiest way to get this. Now blacksmith is not super hard, and if you can get this on blacksmith, more power to you.
But I personally leveled up my rank in blacksmith (not sure if higer rank makes it harder) all the way to 5 trying to get this (that's another achievement, btw). I got to a chain of 9 twice just to fail just before making it. Very frustrating.
Later I got to the woodchopping game (you can do this once you get to Oakvale, not very far in the game). This is much, much easier. Your chain will go up for every single hit rather than every five. The multiplier doesn't go up with it as fast, but you don't need multiplier for this achievement. And it seems to me hitting is much easier to begin with, I didn't miss a single time before getting this achievement while chopping wood.